KRASNAYA POLYANA, Russia — Carina Vogt of Germany has never won a World Cup event but she now owns women’s ski jumping’s first-ever Olympic gold medal.
Sara Takanashi, the World Cup leader in the sport, had been the heavy favorite heading into the Sochi Games, but the 22-year-old Vogt performed when it counted Tuesday, scoring 247.4 points on the normal hill at the RusSki Gorki Jumping Center.
Daniela Iraschko-Stolz of Austria took silver and Coline Mattell of France earned bronze. Takanashi was left in a disappointing fourth.
Sarah Hendrickson, the 19-year-old defending world champion from Park City, Utah, finished 21st of 30 starters, clearly still affected by right knee surgery she underwent in August. Although she showed improved form Tuesday, she plans to take the rest of the season off.
Two other Americans from Park City competed: Jessica Jerome was 10th and former world champion Lindsey Van 15th.
Vogt, who has four second-place finishes in World Cup events this year, had been quiet in training runs, allowing Takanashi and Iraschko-Stolz to take much of the hype as they dueled for supremacy.
‘‘I can’t find the right words,’’ Vogt said. ‘‘I’m just speechless because training yesterday was not so good. Now I’ve improved today. I’ve not won a World Cup till now. It’s unbelievable. I wouldn’t have imagined that one day before.’’
In 2011, the International Olympic Committee agreed to allow the women to compete in ski jumping at Sochi — 90 years after men did at the inaugural Winter Games in 1924.
Takansashi set the tone early, jumping last in the warm-up and beating Iraschko-Stolz by a meter.
When Takanashi’s placing lit up the scoreboard, a group of Japanese fans blew kazoo-like devices and waved a large flagpole containing a carp kite — a fish that the Japanese consider good luck — followed by the Japanese flag, and then a banner with Takanashi’s picture on it.
The carp didn’t bring her much luck.
Takanashi finished the first round in third place, meaning she would jump third-last in the final round, a place she was not used to, considering she has led and won so many World Cups this year.
Iraschko-Stolz took the lead with three jumpers to go, leaving Vogt needing a good jump to overtake her. It wasn’t as good as the Austrian’s final jump, but enough to give the German a 6-point edge.
Japan had been counting on Takanashi to end a gold medal drought. The country’s last gold came at the 2006 Turin Games when Shizuka Arakawa won the ladies singles in figure skating.
‘‘I couldn’t jump the way I wanted to on both attempts.’’ Takanashi said. ‘‘I came here wanting to do my best. I’m incredibly disappointed.’’
Before the final, Jerome’s father Peter held a news conference with other American families who had led the fight to get women’s jumping into the Games.
‘‘No one handed this to them,’’ he said. ‘‘Being good at this didn’t get them to where they are tonight. They were jumping as much as they could because they loved the sport and there was no reward other than the personal satisfaction of competing with their peers, challenging themselves and doing well.’’